2024/08/19 by Stefania Bellavia, Bellavia, Stefania, Greta Malaspina +1 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #Distributed Control Multi-Agent Systems #FOS: Mathematics #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2408.10078
openalex publication_date 2024/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consensus based optimization is a derivative-free particles-based method for the solution of global optimization problems. Several versions of the method have been proposed in the literature, and different convergence results have been proved. However, all existing results assume the objective function to be evaluated exactly at each iteration of the method. In this work, we extend the convergence analysis of a discrete-time CBO method to the case where only a noisy stochastic estimator of the objective function can be computed at a given point. In particular we prove that under suitable assumptions on the oracle's noise, the expected value of the mean squared distance of the particles from the solution can be made arbitrarily small in a finite number of iterations. Numerical experiments showing the impact of noise are also given.